ECE155A Vlad Dorfman Class 10 - Solutions
Problem 1. Noise Enhancement Introduction: The problem illustrates the noise enhancement for a continuous ZF filter using the example of the Lorentzian channe
ECE155A PROBLEMS Vlad Dorfman Class #10 Due: 2/19/07
1. Noise Enhancement. Let s(t) be the Lorentzian step response of the channel ( s(t) = 1/(1+(2*t/PW50)^2) ), and suppose we design a zero-forcing l
ECE155A Fall 07 Equalization Homework Solutions
Part I (Homework 1)
1. Note: This problem is not very clear stated. Therefore the points wont be counted. The question is restated as following: Find Z-
1
Mapping User Data to Magnetic Media
Two different conventions are used to map a binary sequence, z0z1, where zi=0,1 to a magnetization pattern, w0w1, where wi=-1,+1. NRZ: zi=1 -> wi=1 , zi=0 -> wi=
ECE 154B Winter 2007 Homework #1 Due: Monday, January 22 1. In order to do some simulations, one must be able to generate samples of random variables with arbitrary probability distributions. Most pro
ECE 154B Winter 2007 Homework #2 Due: Monday, January 29 1. Consider the 2 hypotheses problem where the a priori probabilities for the two hypotheses are: 0 = and 1 = . Let the conditional probability
ECE 154B Winter 2007 Homework #3 Due: Monday, February 5, 2007 1. Prove that for M a positive even integer, 12 +32+(M-3)2 + (M-1)2 = M(M2-1)/6. (Hint: Use induction) 2. The following applies to M= 4,
ECE 154B Homework #4 Due: February 12, 2007 1. Problem 8.1 from Ziemer and Tranter 2. Problem 8.12 from Ziemer and Tranter 3. Problem 8.13 from Ziemer and Tranter 4. Problem 8.17 from Ziemer and Trant
ECE 154B Winter 2007 Homework #5: Due February 28, 2007 1. Consider that the Voronoi region for a 2-D signal is a hexagon centered at the signal point with shortest distance from the center to any of
ECE 154B Homework #6 Due March 7, 2007 1. Making the usual assumptions of equally likely signals in AWGN and an optimal receiver, it can be shown that the probability of symbol error for M/2 orthogona
ECE 154B Homework #7 Due March 14, 2007 1. Consider the transmission of two FSK sinusoidal signals whose frequencies are chosen
such that the signals are orthogonal. Let the amplitude of each signal b
ECE 154B Winter 2007 Homework #1 Solutions 1. In order to do some simulations, one must be able to generate samples of random variables with arbitrary probability distributions. Most programming langu
ECE 154B Winter 2007 Homework #2 Solutions 1. Consider the 2 hypotheses problem where the a priori probabilities for the two hypotheses are: 0 = and 1 = . Let the conditional probability densities of
ECE 154B Winter 2007 Homework #3 Due: Monday, February 5, 2007 1. Prove that for M a positive even integer, 12 +32+(M-3)2 + (M-1)2 = M(M2-1)/6. (Hint: Use induction) Proof by induction: Let M=2. (2-1)
ECE 154B Homework #4 Due: February 12, 2007 1. Problem 8.1 from Ziemer and Tranter Rb = log 2 M R s bps M = 4 , Rb= 2 2000= 4000 bps M =8 , Rb=3 2000 =6000 bps M =64 , Rb=6 2000 =12000 bps 2. Problem
ECE 154B Homework #6 Solutions 1. Making the usual assumptions of equally likely signals in AWGN and an optimal receiver, it can be shown that the probability of symbol error for M/2 orthogonal signal
ECE 154B Homework #7 Solutions 1. Consider the transmission of two FSK sinusoidal signals whose frequencies are chosen
such that the signals are orthogonal. Let the amplitude of each signal be A, the
ECE155A Fall 07 Lecturer Dr. Vlad Dorfman Class #8
Equalization - Homework Due Oct 29, 2007, 10 points each
1. Find Z-transform and DTFT of am u(n), |a|<1, u(n) is a step function , u(n) =0 for n<0 an